{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import string\n",
    "import os\n",
    "import sys\n",
    "import random\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Meal Item Price Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#The true prices used by the cashier\n",
    "p_fish = 150;p_chips = 50;p_ketchup = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#sample meal prices: generate data meal prices for 5 days.\n",
    "np.random.seed(100)\n",
    "portions = np.random.randint(low=1, high=10, size=3 )\n",
    "portions\n",
    "X = [];y = [];days=10\n",
    "for i in range(days):\n",
    "    portions = np.random.randint(low=1, high=10, size=3 )\n",
    "    price = p_fish * portions[0] + p_chips * portions[1] + p_ketchup * portions[2]    \n",
    "    X.append(portions)\n",
    "    y.append(price)\n",
    "    \n",
    "X = np.array(X)\n",
    "y = np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[8 8 1]\n",
      " [5 3 6]\n",
      " [3 3 3]\n",
      " [2 1 9]\n",
      " [5 1 7]\n",
      " [3 5 2]\n",
      " [6 4 5]\n",
      " [5 4 8]\n",
      " [2 2 8]\n",
      " [8 1 3]] [1700 1500  900 1250 1500  900 1600 1750 1200 1550]\n"
     ]
    }
   ],
   "source": [
    "print (X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Create a linear model\n",
    "from keras.layers import Input, Dense , Activation\n",
    "from keras.models import Model\n",
    "from keras.optimizers import SGD\n",
    "from keras.callbacks import Callback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "price_guess = [np.array([[ 50 ],\n",
    "        [   50],\n",
    "        [  50 ]]) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_input = Input(shape=(3,), dtype='float32')\n",
    "model_output = Dense(1, activation='linear', use_bias=False, \n",
    "                     name='LinearNeuron',\n",
    "                     weights=price_guess)(model_input)\n",
    "sgd = SGD(lr=0.01)\n",
    "model = Model(model_input, model_output)\n",
    "model.compile(loss=\"mean_squared_error\", optimizer=sgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_3 (InputLayer)         (None, 3)                 0         \n",
      "_________________________________________________________________\n",
      "LinearNeuron (Dense)         (None, 1)                 3         \n",
      "=================================================================\n",
      "Total params: 3\n",
      "Trainable params: 3\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/30\n",
      " - 0s - loss: 566500.0000\n",
      "Epoch 2/30\n",
      " - 0s - loss: 38576.1797\n",
      "Epoch 3/30\n",
      " - 0s - loss: 9320.0059\n",
      "Epoch 4/30\n",
      " - 0s - loss: 6873.8545\n",
      "Epoch 5/30\n",
      " - 0s - loss: 5998.2480\n",
      "Epoch 6/30\n",
      " - 0s - loss: 5313.0757\n",
      "Epoch 7/30\n",
      " - 0s - loss: 4722.4736\n",
      "Epoch 8/30\n",
      " - 0s - loss: 4205.7593\n",
      "Epoch 9/30\n",
      " - 0s - loss: 3750.5259\n",
      "Epoch 10/30\n",
      " - 0s - loss: 3347.5698\n",
      "Epoch 11/30\n",
      " - 0s - loss: 2989.7495\n",
      "Epoch 12/30\n",
      " - 0s - loss: 2671.2886\n",
      "Epoch 13/30\n",
      " - 0s - loss: 2387.4255\n",
      "Epoch 14/30\n",
      " - 0s - loss: 2134.1394\n",
      "Epoch 15/30\n",
      " - 0s - loss: 1907.9807\n",
      "Epoch 16/30\n",
      " - 0s - loss: 1705.9363\n",
      "Epoch 17/30\n",
      " - 0s - loss: 1525.3795\n",
      "Epoch 18/30\n",
      " - 0s - loss: 1363.9904\n",
      "Epoch 19/30\n",
      " - 0s - loss: 1219.7112\n",
      "Epoch 20/30\n",
      " - 0s - loss: 1090.7164\n",
      "Epoch 21/30\n",
      " - 0s - loss: 975.3729\n",
      "Epoch 22/30\n",
      " - 0s - loss: 872.2355\n",
      "Epoch 23/30\n",
      " - 0s - loss: 780.0092\n",
      "Epoch 24/30\n",
      " - 0s - loss: 697.5385\n",
      "Epoch 25/30\n",
      " - 0s - loss: 623.7888\n",
      "Epoch 26/30\n",
      " - 0s - loss: 557.8368\n",
      "Epoch 27/30\n",
      " - 0s - loss: 498.8590\n",
      "Epoch 28/30\n",
      " - 0s - loss: 446.1151\n",
      "Epoch 29/30\n",
      " - 0s - loss: 398.9506\n",
      "Epoch 30/30\n",
      " - 0s - loss: 356.7720\n"
     ]
    }
   ],
   "source": [
    "history = model.fit(X, y, batch_size=20, epochs=30,verbose=2)\n",
    "l4  = history.history['loss']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[50.],\n",
       "        [50.],\n",
       "        [50.]], dtype=float32)]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.get_layer('LinearNeuron').get_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### XOR Problem in Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.array([[0,0],[0,1],[1,0],[1,1]])\n",
    "y = np.array([[0],[1],[1],[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#XOR is not a linearly seperable problem\n",
    "#Lets try Linear Model  & see its not working. Add a non-linear layer\n",
    "\n",
    "\n",
    "model_input = Input(shape=(2,), dtype='float32')\n",
    "z = Dense(2,name='HiddenLayer', kernel_initializer='ones', activation='relu')(model_input)\n",
    "#z = Activation('relu')(z)\n",
    "z = Dense(1, name='OutputLayer')(z)\n",
    "model_output = Activation('sigmoid')(z)\n",
    "model = Model(model_input, model_output)\n",
    "#model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sgd = SGD(lr=0.5)\n",
    "#model.compile(loss=\"mse\", optimizer=sgd)\n",
    "model.compile(loss=\"binary_crossentropy\", optimizer=sgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Predictions</th>\n",
       "      <th>Y_actual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>[0.107]</td>\n",
       "      <td>[0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>[0.97]</td>\n",
       "      <td>[1]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>[0.97]</td>\n",
       "      <td>[1]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>[0.021]</td>\n",
       "      <td>[0]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Predictions Y_actual\n",
       "0     [0.107]      [0]\n",
       "1      [0.97]      [1]\n",
       "2      [0.97]      [1]\n",
       "3     [0.021]      [0]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y, batch_size=4, epochs=200,verbose=0)\n",
    "preds = np.round(model.predict(X),decimals=3)\n",
    "pd.DataFrame({'Y_actual':list(y), 'Predictions':list(preds)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[2.1339474, 2.8275306],\n",
       "        [2.1339474, 2.8275306]], dtype=float32),\n",
       " array([-0.02101079, -2.852592  ], dtype=float32),\n",
       " array([[ 2.6571717],\n",
       "        [-4.6348715]], dtype=float32),\n",
       " array([-2.1213162], dtype=float32)]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hidden_layer_output = Model(inputs=model.input,\n",
    "                                 outputs=model.get_layer('HiddenLayer').output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "projection = hidden_layer_output.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0] [0. 0.]\n",
      "[0 1] [2.1129365 0.       ]\n",
      "[1 0] [2.1129365 0.       ]\n",
      "[1 1] [4.246884  2.8024693]\n"
     ]
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    print (X[i], projection[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(5,10))\n",
    "ax = fig.add_subplot(211)\n",
    "plt.scatter(x=projection[:, 0], y=projection[:, 1], c=('g'))\n",
    "\n",
    "ax.set_xlabel('X axis (h1)')\n",
    "ax.set_ylabel('Y axis (h2)')\n",
    "ax.set_label('Transformed Space')\n",
    "\n",
    "#hidden layer transforming the input to a linearly seperable.\n",
    "x1, y1 = [projection[0, 0]-0.5, projection[3, 0]], [projection[0, 1]+0.5, projection[3, 1]+0.5]\n",
    "plt.plot(x1, y1)\n",
    "for i, inputx in enumerate(X):\n",
    "    ax.annotate(str(inputx), (projection[i, 0]+0.1,projection[i, 1]))\n",
    "ax = fig.add_subplot(212)\n",
    "ax.set_label('Original Space')\n",
    "plt.scatter(x=X[:, 0], y=X[:, 1], c=('b'))\n",
    "for i, inputx in enumerate(X):\n",
    "    ax.annotate(str(inputx), (X[i, 0]+0.05,X[i, 1]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qIvuEHqr1ycuLN3LLUwtp2SyFaeNGcFyfTmGXJCJJRqEag9Kycn736goefHsN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\nRUQC9P8B73+RepCEQzwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c83e20edd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -2.78249192e+00,   1.45849399e-03],\n",
       "       [ -2.78954506e-02,   1.96480966e+00],\n",
       "       [ -2.78954506e-02,   1.96480966e+00],\n",
       "       [  2.72670102e+00,   3.92816067e+00]], dtype=float32)"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Logistic neuron: Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "data = load_breast_cancer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = data.data\n",
    "y = data.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.30, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(398, 30)"
      ]
     },
     "execution_count": 425,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 459,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model_input = Input(shape=(30,), dtype='float32')\n",
    "\n",
    "model_output = Dense(1, activation='sigmoid',\n",
    "                     name='SigmoidNeuron')(model_input)\n",
    "sgd = SGD(lr=0.01)\n",
    "model = Model(model_input, model_output)\n",
    "model.compile(loss=\"binary_crossentropy\", optimizer=sgd, metrics=[\"accuracy\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 398 samples, validate on 171 samples\n",
      "Epoch 1/5\n",
      "0s - loss: 0.6121 - acc: 0.6759 - val_loss: 0.4414 - val_acc: 0.8655\n",
      "Epoch 2/5\n",
      "0s - loss: 0.3767 - acc: 0.8518 - val_loss: 0.3202 - val_acc: 0.9181\n",
      "Epoch 3/5\n",
      "0s - loss: 0.2976 - acc: 0.8995 - val_loss: 0.2631 - val_acc: 0.9415\n",
      "Epoch 4/5\n",
      "0s - loss: 0.2562 - acc: 0.9171 - val_loss: 0.2282 - val_acc: 0.9532\n",
      "Epoch 5/5\n",
      "0s - loss: 0.2296 - acc: 0.9246 - val_loss: 0.2036 - val_acc: 0.9532\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x28a1d474748>"
      ]
     },
     "execution_count": 460,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "model.fit(scaler.fit_transform(X_train), y_train, batch_size=10, epochs=5,verbose=2,\n",
    "          validation_data=(scaler.fit_transform(X_test), y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from scipy import stats \n",
    "\n",
    "from sklearn.datasets.samples_generator import make_regression \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m=82.90456141637904, c=-3.709228868670303\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ecc6a0bef0>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, y = make_regression(n_samples = 100, \n",
    "                       n_features=1, \n",
    "                       n_informative=1, \n",
    "                       noise=20,\n",
    "                       random_state=2017)\n",
    "x = x.flatten()\n",
    "slope, intercept, _,_,_ = stats.linregress(x,y)\n",
    "print(\"m={}, c={}\".format(slope,intercept))\n",
    "best_fit = np.vectorize(lambda x: x * slope + intercept)\n",
    "plt.plot(x,y, 'o', alpha=0.5)\n",
    "grid = np.arange(-3,3,0.1)\n",
    "plt.plot(grid,best_fit(grid), '.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tu7jmbDVZMNDZVfKpSKmj6/EZGfJiBHarOXmf3BtNpWJQE5FuVNNxrNptW/NyEO9HD0LG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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ecc6330b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Descent: -3.73, 82.80 73\n",
      "Least Squares: -3.71, 82.90\n"
     ]
    }
   ],
   "source": [
    "def gradient_descent(x, y, theta_init, step=0.1, maxsteps=0, precision=0.001, ):\n",
    "    costs = []\n",
    "    m = y.size # number of data points\n",
    "    theta = theta_init\n",
    "    history = [] # to store all thetas\n",
    "    preds = []\n",
    "    counter = 0\n",
    "    oldcost = 0\n",
    "    pred = np.dot(x, theta)\n",
    "    error = pred - y \n",
    "    currentcost = np.sum(error ** 2) / (2 * m)\n",
    "    preds.append(pred)\n",
    "    costs.append(currentcost)\n",
    "    history.append(theta)\n",
    "    counter+=1\n",
    "    while abs(currentcost - oldcost) > precision:\n",
    "        oldcost=currentcost\n",
    "        gradient = x.T.dot(error)/m \n",
    "        theta = theta - step * gradient  # update\n",
    "        history.append(theta)\n",
    "        \n",
    "        pred = np.dot(x, theta)\n",
    "        error = pred - y \n",
    "        currentcost = np.sum(error ** 2) / (2 * m)\n",
    "        costs.append(currentcost)\n",
    "        \n",
    "        if counter % 25 == 0: preds.append(pred)\n",
    "        counter+=1\n",
    "        if maxsteps:\n",
    "            if counter == maxsteps:\n",
    "                break\n",
    "        \n",
    "    return history, costs, preds, counter\n",
    "xaug = np.c_[np.ones(x.shape[0]), x]\n",
    "theta_i = [-15, 40] + np.random.rand(2)\n",
    "history, cost, preds, iters = gradient_descent(xaug, y, theta_i, step=0.1)\n",
    "theta = history[-1]\n",
    "print(\"Gradient Descent: {:.2f}, {:.2f} {:d}\".format(theta[0], theta[1], iters))\n",
    "print(\"Least Squares: {:.2f}, {:.2f}\".format(intercept, slope))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "def error(X, Y, THETA):\n",
    "    return np.sum((X.dot(THETA) - Y)**2)/(2*Y.size)\n",
    "\n",
    "ms = np.linspace(theta[0] - 20 , theta[0] + 20, 20)\n",
    "bs = np.linspace(theta[1] - 40 , theta[1] + 40, 40)\n",
    "\n",
    "M, B = np.meshgrid(ms, bs)\n",
    "\n",
    "zs = np.array([error(xaug, y, theta) \n",
    "               for theta in zip(np.ravel(M), np.ravel(B))])\n",
    "Z = zs.reshape(M.shape)\n",
    "\n",
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.plot_surface(M, B, Z, rstride=1, cstride=1, color='b', alpha=0.2)\n",
    "ax.contour(M, B, Z, 20, color='b', alpha=0.5, offset=0, stride=30)\n",
    "\n",
    "\n",
    "ax.set_xlabel('Intercept')\n",
    "ax.set_ylabel('Slope')\n",
    "ax.set_zlabel('Cost')\n",
    "ax.view_init(elev=30., azim=30)\n",
    "ax.plot([theta[0]], [theta[1]], [cost[-1]] , markerfacecolor='r', markeredgecolor='r', marker='o', markersize=7);\n",
    "#ax.plot([history[0][0]], [history[0][1]], [cost[0]] , markerfacecolor='r', markeredgecolor='r', marker='o', markersize=7);\n",
    "\n",
    "\n",
    "ax.plot([t[0] for t in history], [t[1] for t in history], cost , markerfacecolor='r', markeredgecolor='r', marker='.', markersize=2);\n",
    "ax.plot([t[0] for t in history], [t[1] for t in history], 0 , markerfacecolor='r', markeredgecolor='r', marker='.', markersize=2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5sQhispYo+re0ZqdJaTLLcrC62sTDDy8kzr048AVkv3AQUaGjluaxLBd37li4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VtFoH43A4qVQgk8nV+MHUJ2WbJMjlcpPP5ygWi3W5aBtBZC05rHZGbQXhciAIjr2O+FTdmNcn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\nLNbMDn7tAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ecc614de48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Xu07p9GLcZquA0bgGRuMq1NWtgsmUC/FsUiM4eAjCwi5DWNhlCAkZxlnhz1NYVDGyQ+RE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\nfzc1Nfnm5s6QuXPnEgCqra1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niaeFJInUTjt3ivUEn3lGrC+Yny+3ZT4mNVU8O1UqIawK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\naFKllFJKKRUH/x/MEhUOUSaTSQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c82f3b7550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 5))\n",
    "ax = fig.add_subplot(111)\n",
    "xlist = np.linspace(-7.0, 7.0, 100) # Create 1-D arrays for x,y dimensions\n",
    "ylist = np.linspace(-7.0, 7.0, 100)\n",
    "X,Y = np.meshgrid(xlist, ylist) # Create 2-D grid xlist,ylist values\n",
    "Z = 50 - X**2 - 2*Y**2  # Compute function values on the grid\n",
    "plt.contour(X, Y, Z, [10,20,30,40], colors = ['y','orange','r','b'], linestyles = 'solid')\n",
    "ax.annotate('Direction Of Gradident', xy=(.6, 0.3), xytext=(.6, 0.3))\n",
    "ax.annotate('Temp=30', xy=(2.8, 2.5), xytext=(2.8, 2.5))\n",
    "ax.annotate('Temp=40', xy=(2.3, 2), xytext=(2.3, 1.5))\n",
    "#ax.arrow(0, 0, 6.9, 6.8, head_width=0.5, head_length=0.5, fc='k', ec='k')\n",
    "ax.arrow(2, 1.75, 2*2/20, 4*1.75/20, head_width=0.2, head_length=0.5, fc='r', ec='r')\n",
    "ax.arrow(2, 1.75, -2*2/10, -4*1.75/10, head_width=0.3, head_length=0.5, fc='g', ec='g')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39.875"
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "50 - 2**2 - 2*1.75**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Osk9UNBKRTHI5kAMcBZwOZJvZIcU11KL8kggLFy7kww8/pFOnTqGjiEiKW7ly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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8455b3a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "\n",
    "def step(x):\n",
    "    return np.array(x > 0, dtype=np.int)\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(0, x)\n",
    "\n",
    "def tanh(x):\n",
    "    return (np.exp(x)-np.exp(-x)) / (np.exp(x) + np.exp(-x))\n",
    "\n",
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "y_step = step(x)\n",
    "y_sigmoid = sigmoid(x)\n",
    "y_relu = relu(x)\n",
    "y_tanh = tanh(x)\n",
    "fig, axes = plt.subplots(ncols=4, figsize=(20, 5))\n",
    "ax = axes[0]\n",
    "ax.plot(x, y_step,label='Binary Threshold',  color='k', lw=1, linestyle=None)\n",
    "ax.set_ylim(-0.8,2)\n",
    "ax.set_title('Binary Threshold')\n",
    "\n",
    "ax = axes[1]\n",
    "ax.plot(x, y_sigmoid,label='Sigmoid',  color='k', lw=1, linestyle=None)\n",
    "ax.set_ylim(-0.001,1)\n",
    "ax.set_title('Sigmoid')\n",
    "\n",
    "ax = axes[2]\n",
    "ax.plot(x, y_tanh,label='Tanh',  color='k', lw=1, linestyle=None)\n",
    "ax.set_ylim(-1.,1)\n",
    "ax.set_title('Tanh')\n",
    "\n",
    "ax = axes[3]\n",
    "ax.plot(x, y_relu,label='ReLu',  color='k', lw=1, linestyle=None)\n",
    "ax.set_ylim(-0.8,5)\n",
    "ax.set_title('ReLu')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dd94JOwqQcvLz8/Xzn//8uPFiYQ7gjzVKGQDEEKcwgdgpPl6sc+fOSTterCI4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8473df898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-10.0, 10.0, 0.1)\n",
    "def lineup(x):\n",
    "    return (x-4)/12-1\n",
    "\n",
    "def cliff(x):\n",
    "    x1 = -tanh(x[x<4])\n",
    "    x2 = np.apply_along_axis(lineup, 0, x[x>4])\n",
    "    return np.concatenate([x1, x2])\n",
    "y_cliff = cliff(x)\n",
    "\n",
    "    \n",
    "fig, axes = plt.subplots(ncols=1, figsize=(10, 5))\n",
    "ax = axes\n",
    "ax.plot(x, y_cliff,label='Steep Cliff',  color='k', lw=1, linestyle=None)\n",
    "ax.set_ylim(-1.,1)\n",
    "ax.set_title('Steep Cliff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial curve fitting: Model Capacity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from math import sin, pi\n",
    "N = 100; max_degree = 20\n",
    "noise = np.random.normal(0, 0.2, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1df3ef50a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame( index=list(range(N)),columns=list(range(1,max_degree)))\n",
    "for i in range(N):\n",
    "    df.loc[i]=[pow(i/N,n) for n in range(1,max_degree)]\n",
    "df['y']=[sin(2*pi*x/N)+noise[x] for x in range(N)]\n",
    "\n",
    "plt.scatter(x=df[1], y=df['y'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from keras.initializers import RandomNormal\n",
    "degree = 3\n",
    "X = df[list(range(1,degree+1))].values\n",
    "y = df['y'].values\n",
    "X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.60, random_state=42)\n",
    "model_input = Input(shape=(degree,), dtype='float32')\n",
    "model_output = Dense(1, activation='linear', name='LinearNeuron')(model_input)\n",
    "sgd = SGD(lr=0.4)\n",
    "model = Model(model_input, model_output)\n",
    "model.compile(loss=\"mean_squared_error\", optimizer=sgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "history = model.fit(X_train,y_train , batch_size=10, epochs=4000,verbose=0, validation_data=(X_test,y_test) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AmoA7fL7pAq2ruPO/rjWxMubkHx8Pfw5X5/np+Asd3TzpWMcz64O1MCuNYPKb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\nQtiyqaAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1df3f1afa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = model.predict(X_train)\n",
    "plt.scatter(X_train[:,0], y_train)\n",
    "plt.plot(np.sort(X_train[:,0]), y_pred[X_train[:,0].argsort()], label='poly fit')\n",
    "plt.plot(np.sort(X_train[:,0]), [sin(2*pi*x) for x in np.sort(X_train[:,0]).tolist()], label='sin (actual pattern)')\n",
    "plt.title(\"Model fit for polynomial of degree {}\".format(degree))\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[  7.2821503],\n",
       "        [-23.939705 ],\n",
       "        [ 16.676823 ]], dtype=float32), array([0.3239697], dtype=float32)]"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 939,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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leQK/Gz8AEXsuIMp3z6/cS/PEOG4a2tm2GDQBKBWB7h3di5Lyaub8ezepyYn8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\nCcVWnpAIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c85f707b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = model.predict(X_test)\n",
    "plt.scatter(X_test[:,0], y_test)\n",
    "plt.plot(np.sort(X_test[:,0]), y_pred[X_test[:,0].argsort()])\n",
    "plt.title(\"Model fit for plynomial of degree {}\".format(degree))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
